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Let $K$ be a finite extension of $\Q_p$, and $K^{un}$ its unramified subfield. The unramified degree of $K$ is the degree $[K^{un}:\Q_p]$, which is equal to its residue field degree.

Since $\Q_p$ has a unique unramified extension of degree $n$ for each positive integer $n$, the unramified degree of an extension determines its unramified subfield.

The Galois unramified degree of $K$ is the unramified degree of its Galois closure.

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  • Review status: reviewed
  • Last edited by Andrew Sutherland on 2021-05-14 21:30:55
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